Entropy and quasimorphisms
Entropy and quasimorphisms
Let $ S $ be a compact oriented surface. We construct homogeneous quasimorphisms on $ {\rm Diff}(S, \operatorname{area}) $, on $ {\rm Diff}_0(S, \operatorname{area}) $, and on $ {\rm Ham}(S) $, generalizing the constructions of Gambaudo-Ghys and Polterovich.We prove that there are infinitely many linearly independent homogeneous quasimorphisms on $ …